Is linear sketching over F2 optimal for one-way XOR communication?

Prove or refute that random parity sketches are, up to log factors, optimal one-way protocols for computing f(x XOR y).

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "computer-science",
	3	+ "topics": [
	4	+ "algorithms-complexity"
	5	+ ],
	6	+ "type": "proof",
	7	+ "source": {
	8	+ "key": "sublinear",
	9	+ "name": "Sublinear.info",
	10	+ "url": "https://sublinear.info/78",
	11	+ "id": "78",
	12	+ "curator": "Sublinear.info editors",
	13	+ "poser": "Grigory Yaroslavtsev",
	14	+ "status": "open",
	15	+ "as_of": "2026-10-20",
	16	+ "catalog": "0521c19bbd38"
	17	+ }
	18	+}